What is meant by the 95% confidence interval of the mean ?
That 95% of my sample is OK to do more tests.
That I am 95% confident that the confidence interval will contain the parameter being estimated.
That 5% of my sample is not OK.
That I am 95% sure that the population mean is 95.
Check out the second choice.
The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?
The correct answer is: "That I am 95% confident that the confidence interval will contain the parameter being estimated."
The 95% confidence interval of the mean is a statistical measure that provides an estimated range within which the true population mean is likely to fall. It is not related to the percentage of your sample that is OK or not OK, nor does it provide certainty about the value of the population mean. Instead, it indicates a level of confidence (95%) that the true population mean will lie within the calculated interval.
The correct answer is:
"That I am 95% confident that the confidence interval will contain the parameter being estimated."
When we talk about a 95% confidence interval of the mean, it means we are estimating a range of values within which the true population mean is likely to lie, with 95% confidence. It does not mean that 95% of the sample is okay, or that 5% of the sample is not okay.
To calculate the 95% confidence interval, we need to collect a sample and compute its mean and standard deviation. Then, using statistical methods, we can calculate a range of values around the sample mean that is likely to contain the true population mean.
The concept of confidence level, in this case 95%, refers to the level of confidence we have that the confidence interval contains the true population parameter. In other words, if we were to repeat the sampling process multiple times and construct a confidence interval for each sample, 95% of those intervals would contain the true population mean.
Therefore, it is important to understand that the confidence interval estimates our level of confidence in capturing the true population mean, rather than saying whether the sample is good or bad.